I did eventually get it to work on my FireStick, but not for a couple of hours.

Oddly enough, I just now received an email from Amazon saying “We noticed you recently experienced poor video playback on Amazon Video” and they refunded me. I never contacted them or complained on Amazon. I guess they can either tell from their end that I kept trying and failing to get past the first frame of the movie on the FireStick, or maybe the fact that I tried to watch it on my laptop, my Fire tablet, my living room FireStick and my bedroom FireStick within about 10 minutes alerted them to the fact that something had gone sideways.